In many electric circuits including so-called integrated circuits, i.e., ICs, a fully integrated oscillator is needed for generating a reference clock signal with high frequency accuracy and with very low temperature and long-term drift. Clock signal generators are known to be used for a variety of applications, for example, for digital signal processing circuits. Highly accurate clock signal generators are typically used in analog-to-digital devices, i.e., for sampling an analog signal to produce a corresponding digital signal.
In conventional applications and for this purpose relaxation oscillators have been used, which exhibit low complexity and can be easily adjusted or programmed. However, a drift in frequency typically does not only originate from parameter changes of the primary passive frequency determining components like resistors and capacitors. Also active circuit components such as transistors in current mirrors, switches and comparators may cause a drift in frequency effectuated by temperature influence or stress on the components.
To a large extent this additional drift in frequency effectuated by parameter changes of active circuit components can be avoided through use of a harmonic oscillator comprising a resonator having a high quality factor wherein it is assumed that the active circuit portion fulfills some minimum requirements. In the case of a Wien-bridge oscillator and when operated at oscillation frequency the amplifier stage must comply with a minimum amplification and a maximum phase shift, in order to stay below a predefined maximum frequency drift of, for example, ±1%. As long as the minimum requirements are fulfilled the high quality factor of the resonator provides for corresponding high frequency stability. The quality of an open oscillatory circuit system is a measure of the capability of the closed oscillatory to suppress variations in the oscillation frequency. Then the drift in frequency is substantially independent of parameter changes of the active components and is caused primarily by temperature variations of the passive circuit devices.
In the following and with reference to FIG. 1 the basic properties of a Wien-bridge oscillator 110 are described wherein a conventional Wien-bridge 110 shown in the dotted circle.
The resonant frequency ωr of the Wien-bridge is determined by resistors R1, R2 and capacitors C1, C2 as
      ω    r    =      1                  R        ⁢                                  ⁢                  1          ·          R                ⁢                                  ⁢                  2          ·          C                ⁢                                  ⁢                  1          ·          C                ⁢                                  ⁢        2            wherein in many applications the values of the components is chosen as R1=R2=R and C1=C2=C. Consequently the resonant frequency is determined by
      ω    r    =      1          R      ⁢                          ⁢      C      
The complex transfer function normalized to the resonant frequency is
                              F          ⁡                      (                          s              =              jΩ                        )                          =                              -                          1                              3                +                ɛ                                              ·                                    1              -                              Ω                2                            -              jɛΩ                                      1              -                              Ω                2                            +                              3                ⁢                jΩ                                                                        (        1        )            wherein
      Ω    =          ω              ω        r              ,and wherein variable ε is a positive number, ε<1, and that describes the detune of the bridge circuit.
From equation (1) the frequency response Φ of the phase shifting follows as
  Φ  =      arctan    ⁡          [                        -                      (                          3              +              ɛ                        )                          ⁢                              Ω            ⁡                          (                              1                -                                  Ω                  2                                            )                                                                          (                                  1                  -                                      Ω                    2                                                  )                            2                        -                          3              ⁢                              ɛΩ                2                                                        ]      
FIGS. 2a and 2b depict the frequency response of the amplitude (magnitude) and of the phase shifting (phase) for ε= 1/15. FIG. 2c illustrates the relation between phase shifting and detune ε (eps) in a frequency range of about ±2% around the resonant frequency.
As shown in FIG. 2b the frequency response of the phase shifting exhibits a steep slope around normalized resonant frequency. Based on this property, high-quality oscillators, i.e., oscillators exhibiting high stability in frequency, can be implemented based on Wien-bridge resonators. However, a downside of a Wien-bridge oscillator is the attenuation of the signal amplitude at resonant frequency. For calculating the gain of the circuit, we assume that oscillation frequency matches resonant frequency, which is approximately true for a phase shift of less than 10 degrees, confer FIG. 2b, and if the detune ε is small.
In a non-detuned Wien-bridge circuit, i.e., ε=0, the differential output signal would be zero. As a consequence the Wien-bridge necessarily must be detuned slightly in order to comply with the requirement of oscillating with constant amplitude.
The quality factor of a resonant circuit is
  Q  =                    1        2            ⁢                        ⅆ          Φ                          ⅆ          Ω                    ⁢              (                  Ω          =          1                )              =                            1          ɛ                +                  1          3                    ≈              1        ɛ            
Note that generally the quality of a resonant circuit is defined as partial derivative of amplitude and phase at oscillation frequency. Since in the case considered here the partial derivative of the amplitude is zero at resonant frequency, the partial derivative of the phase remains.
Accordingly the correlation between detune and quality, i.e., stability in frequency, of a resonant circuit can be characterized in that the lower the detune, the higher is the quality, i.e., stability in frequency, of the resonant circuit.
The oscillator circuit comprising the Wien-bridge and the amplifier as depicted in FIG. 1 can be simplified to a schematic circuit depicted in FIG. 3. The schematic illustrates a transfer function of the feedback loop and can be analyzed based on the frequency response of the feedback loop amplification T(s):T(s)=A(s)·└Fp(s)−Fn(s)┘=A(s)·F(s)wherein A(s) is the gain of the amplifying element in the circuit and
                    F        p            ⁡              (        s        )              -                  F        n            ⁡              (        s        )              =            F      ⁡              (        s        )              =                  V        br                    V        out            describes the transfer function of the feedback path.
The Barkhausen criterion is a (mathematical) condition to determine when a linear electronic circuit will oscillate and provides the necessary—but not sufficient—conditions for a stable oscillation. More precisely the Barkhausen criterion consists of two conditions, namely:
1. The absolute value of the loop gain in an amplifier with feedback path as depicted in FIG. 3 must be equal to unity in absolute magnitude, i.e.,|T(s=jω0)=1|
2. The phase shift at the oscillating frequency must have a positive feedback. This condition is satisfied when the phase shift is an integer multiple of 360°:∠T(s=jω0)=z·360° wherein z=0, 1, 2, . . .
In this embodiment a phase shift of z=0, i.e., 0° phase shift is considered.
It follows from the amplitude condition, i.e., the first of the above mentioned conditions, that the necessary gain A is higher when the detune is lower.
It can be shown that in a stable oscillating state it follows from the Barkhausen criteria that an amplification of A=(9/ε)+3 is required at the resonant frequency.
As a consequence in Wien-bridges the requirements for the amplifier stage are high, i.e., the amplifier stage must exhibit a high gain while at the same time exhibiting a low phase shift. In one embodiment the absolute value of the phase shift should be below 10° since in this range only a high quality and frequency stability can be achieved, i.e., the frequency response of the phase shift of the Wien-bridge is steep. Consequently the amplifier stage is a crucial component of the oscillator. Drift caused by temperature variation and process parameter variation may have significant influence on the accuracy of the oscillation frequency, as these typically cause significant variations in gain and phase shift in amplifier circuits.
With respect to the quality factor, i.e., stability in frequency, optimum solutions can be achieved by adjusting the detune ε of the Wien-bridge to a value high enough so that the oscillation amplitude exhibits a sufficient high value.
The achieved solution furthermore shall effectuate that the drift in frequency caused by temperature variations as far as possible depends on the temperature coefficients of the resistors in the Wien-bridge instead of depending on any semiconductor component as known from conventional circuits.